From my limited experience with Kontakt.io beacons, I have seen that they do not advertise their presence as frequently as the 10-30Hz iBeacon standard. While slower transmission rates can help make battery-powered beacons last longer, it can slow down background detection on iOS.
Understand that when an iOS app looking for iBeacons is not in the foreground, iOS only does a brief Bluetooth scan periodically to look for iBeacons. If a beacon is not transmitting at that time, it will not be detected. When an app is ranging for iBeacons in the foreground, there is a constant bluetooth scan, so there is much less of a chance of missing infrequent beacon transmissions.
I suspect that if you wait long enough (many minutes or even hours) in the background, the Kontakt.io beacons will eventually be detected. You might check to see if Kontakt.io offers a config option to increase the transmission frequency to help this.